Question: Which decimal is equivalent to $\dfrac{4}{3}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $0.75$ (Choice B) B $1.25$ (Choice C) C $1.\overline{1}$ (Choice D) D $1.\overline{3}$
$ \dfrac{4}{3}$ represents $4 \div 3 $. ${3}$ ${4}$ $\text{How many times does }3\text{ go into }{4}\text{?}$ ${1}$ ${3}$ $-$ ${1}$ ${4}\div3={1}\text{ with a remainder of }{1}$ ${0}$ ${.}$ ${.}$ $\text{Write in a decimal and a zero.}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${3}$ ${9}$ $-$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${3}$ ${9}$ $-$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${3}$ ${9}$ $-$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${3}$ ${9}$ $-$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ $\text{How many times does }3\text{ go into }{10}\text{?}$ ${0}$ ${0}$ ${3}$ ${3}$ ${9}$ $-$ ${1}$ ${1}$ ${10}\div3={3}\text{ with a remainder of }{1}$ Notice how the decimal is repeating and will continue to repeat as we bring down more zeros. So $\dfrac{4}{3}$ is equivalent to $1.\overline{3}$.